Henriksen has been nominated for three Golden Globes. He is often said to be one of only two actors (the other being Bill Paxton) who has been killed on-screen by an Alien, a Predator and a Terminator. However, some argue that Henriksen's character Bishop in Aliens was not killed by an Alien, as he was technically still active after being ripped in two by the Queen.

Henriksen was James Cameron's first choice to play the titular Terminator in The Terminator, when the cyborg conformed to its original concept of being a 'gray man' that could blend into a crowd before striking unexpectedly. Cameron even drew some concept art of Henriksen as the Terminator, but the character was eventually altered, becoming an unstoppable human tank instead of a stealthy infiltrator, and Arnold Schwarzenegger was cast in the role.